Optical absorption and magnetic circular dichroism of MnI2

Physica 121B (1983) 62-80 North-Holland Publishing Company

OPTICAL H.J.W.M.

ABSORPTION HOEKSTRA,

Laboratory of Inorganic The Netherlands Received

6 December

AND MAGNETIC P.R. BOUDEWIJN*,

Chemistry,

Materials

CIRCULAR

DICHROISM

H. GROENIER

Science Center

of the University,

OF MI&

and C. HAAS Nijenborgh

16, 9747 AC

Groningen,

1982

Absorption and Magnetic Circular Dichroism (M.C.D.) spectra of single crystals of MnIr in the spectral region l@XKK34)000 cm-’ at temperatures between 1.5 and 300 K are reported. The observed bands are due to d-d transitions of the Mn2+ ions. Parameters of the electron repulsion, the cubic crystal field and the spin orbit coupling are deduced from the spectra. The transitions are induced by vibronic interactions with ungerade phonons, and by exchange interactions between neighbouring ions. The relative contribution of these two mechanisms is different for different transitions. M.C.D. parameters calculated for a trigonally-anisotropic coupling of Mn*’ with ungerade phonons are compared with the observed spectra. A detailed assignment is given for the fine structure of the ‘Al, + 4AI,, 4E, transitions. These transitions show the effects of exciton diffusion, with an effective exciton hopping integral of 9 cm-‘.

1. Introduction The optical absorption spectra of high-spin 3d” transition metal ions in octahedral coordination have attracted the attention of many investigators [l--8]. This is partly due to the uniqueness of the d5 configuration. In octahedral symmetry all d-d transitions of a high-spin 3d5 ion are both parity and spin forbidden for electric dipole transitions. Nevertheless the d-d transitions of the Mn2+ ion are easily observed in the absorption spectrum. In the literature different mechanisms of intensity borrowing have been proposed to explain the observation of these doubly-forbidden d-d transitions in Mn2+ compounds. The spin-forbiddenness can be relieved by spin-orbit interaction. The parity selection rule for electric dipole transitions is then broken by a vibronic coupling with ungerade vibrational modes. Experimentally it is found that the oscillator strengths of the d-d transitions increase in the sequence MnCl*, MnBr2, MnIz [3,4, S]. This corresponds to the generally observed trend that the intensity increases approximately with l/(AE)2, as the onset AE of strong charge transfer absorption decreases [2]. Thus the intensity comes * Philips Research

Laboratories,

Eindhoven,

0378-4363/83/0000-0000/$03.00

The Netherlands.

@ 1983 North-Holland

from higher levels and the band shift measures the extent of perturbation of these higher levels. Another factor is that the oscillator strength of vibronically induced transitions is related to the magnitude of the spin-orbit coupling of the outer p electrons of the ligand, which increases strongly in the sequence Cl, Br, I. An alternative explanation for the occurrence of strong spin-forbidden d-d absorption bands in manganese compounds is a mechanism which involves the exchange interactions between pairs of Mt?+-ions [2,9, lo]. The spin selection rule for a transition on one ion is relieved by exchange coupling with the neighbouring ions. The fact that exchange interactions can play an important role in optical transitions is demonstrated clearly by the observation of magnon side bands in compounds [S]. transition several metal However, in MnCl*, MnBrz and Mn12, the exchange interactions are weak, as indicated by the very low values of the NCel temperatures TN and the paramagnetic Curie temperatures 0 [12, 131. Therefore, in first instance one would perhaps not expect a large contribution of the mechanism in these compounds. exchange involve transitions However, the optical exchange interactions in the excited states and the magnitude of these is not known. In an effort to determine the mechanism of the

H.J. W.M. Hoekstra

absorption processes in Mn12 we have carried out a study of absorption and magnetic circular dichroism (M.C.D.) spectra of single crystals of MnI*. From absorption spectra only, it is not possible to deduce which mechanism is responsible for the absorption process. However, the M.C.D. is due mainly to transitions induced by vibronic interactions; transitions induced by exchange interactions contribute only weakly to the M.C.D. Sign and magnitude of the M.C.D. are determined by the symmetries of the electronic states involved [ll]. By comparing experimental and theoretical M.C.D. parameters detailed information about the absorption mechanism is obtained. 2. Experimental

(=optical density) and the difference between the absorbance of left- and right-circularly polarized light AA = A_ - A+. The spectrum consists of six bands, with oscillator strengths of about lo-‘, due to d-d transitions of the Mn*‘ions (table I). Several of the bands exhibit at low temperature a pronounced vibronic fine structure. Above 300OOcm-’ the absorption is very strong and probably due to allowed electric dipole transitions. These transitions are due to charge-transfer states, which play an important

-SK

methods

Mn12 has the layer-type Cd(OH)2 structure space group D&. The Mn*+ ions occupy octahedral sites which are only slightly trigonally distorted. Single crystals of Mn12 were grown as described previously [S]. Mn12 is hygroscopic, and all crystal handling had to be performed with the exclusion of moisture and air. For optical measurements crystals with a thickness of 50-200 km for transitions to the quartet states, and of 860 pm for the transition to the *T&I) state were used. All spectra were recorded with the direction of propagation of the light and the applied magnetic field parallel to the c-axis, i.e. perpendicular to the layers. The absorption and M.C.D. spectra were measured using a Perkin-Elmer El monochromator. The crystal was mounted in an Oxford Instruments SM4 cryostat, providing magnetic fields up to 5 T. The temperature could be varied from 1.5 to 300 K. The M.C.D. apparatus was home-built according to the principles described by Collingwood et al. [14]. The spectra were recorded with a spectral resolution of about 1 cm-‘. 3. Experimental

63

of Mnb

et al. I Optical absorption and magnetic circular dichroism

results

The absorption and M.C.D. spectra of Mn12 in the 16000-30000 cm-’ spectral region are given in figs. l-6. As units we used absorbance A

16

18

20

22

24

26

28

32

30

cr (cm-’ .103) Fig. 1. The absorption

-0.5r

spectrum

’ ’ ’ 17Qoa 18000

of MnIZ.

’

’

’

19000 zoow Uicm-11

0

’

21000

1 22000

Fig. 2. Absorption A and M.C.D. AA of the ?&G) (left) and 9&G) (right) transitions of MnIz for H = 4.0 Tesla, T=3.8K (-), T=2.3K (-----) and T= 18SK (.. .). The M.C.D. spectrum at T = 2.3 K should be multiplied by a factor 4. The thickness of the crystal is d = 50 pm.

64

H.J. W.M. Hoekstra

et al. I Optical absorption and magnetic circular dichroism

Table 1 Assignment and comparison between calculated and observed of h4& (t) means maximum of absorption band, (m) means

of MnIz

energy levels that the spin-

orbit component is resolved in the M.C.D. spectrum only and (m)* means that the M.C.D. signal is observed at temperatures below the Neel temperature only. Of the vibronic progressions of the “r,cD) and 4E,(4D) bands the observed energy of the first (strongest) peak is given in both cases. Parameters (cm-‘); 10 Dq = 6083, B = 691, C = 3000, 5 = 695, 5’ = -195 Calculated energy (cm-‘) 17616 17626 17927 18125

Spinorbit component

State

Observed energy (cm-‘)

qd“G)

17600(t)

“Td4G)

20500(t)

Ui,Z E” u;,,

E

20476 20479 20698 20840

E

21891

U

“A,@3

22330

21906 21908 21909

E E U

“EeG)

22047

23938 24688

E” U

25337 25360 25410 25412

E”

26682 26706 26735

E” U E

28044 28066 28534

U E E

29069 29194 29257 29490 29573

Uil2 u/2

E”

Ub2

23856(m) 24625(m)

4T2C4D)

E

25478(m)

UkiZ

E E’ U

25417(m) 25437(m)*

“EeD)

26316(m) 26334(m)* 26372(m)

28910(t)

Uj/Z usi2

E”

role as intermediate states for the doubly forbidden electric dipole d-d transitions. The dominant contribution to the M.C.D. spectrum of Mn12 comes from so-called C terms [ 111. The spin degeneracy of the 6A1, ground state of the

Mn*+ ions is lifted by the applied magnetic field, and the temperature dependence of the M.C.D. is determined by the Boltzmann distribution over the ground state components. In the paramagnetic region, for not too large values of H/T, the

65

H.J. W.M. Hoekstra et al. I Optical absorption and magnetic circular dichroism of MnIz

1.5 -

10 -

05 -

5.0

* I I

b

0

P

o- x

s

L

/-

“,-o.os-010 -0151

22600

-3.0 I

,

Y

II

D

(cm-1

I

I

I

I

1

I

I

I

1

25OM:

24000 CT km-l1

I.

22800

22500

22000

I

23000

1

Fig. 3. Absorption A and M.C.D. AA of the 4A1,, “E&G) band of MnI2 for H = 4.0 Tesla, T = 3.8 K (-) and T = 2.3K(-----); d=50pm.

Fig. 4. Absorption A and M.C.D. AA of the 6A1,+2T$cI) transition of MnI2 for H = 4.0 Tesla and T = 18.8 K; d = 860 Wm.

Do = &c

[I(A&t+lJh)l*+

t(A+-lJh)12]

.

(3)

a,r\ M.C.D.

is given by

AA = y.sh(~)Cgcd(/.~gH,'kT) where h is a line shape energy, H the magnetic thickness of the sample, absorbing centers, y a magneton and CO is given

C, = +

c (AC& A 0,~

,

(1)

function, E the photon field strength, d the c the concentration of constant, pa the Bohr by

+ 2S,IAa)

x [I(Aalm+lJh)l*

- I(A+KIJA)~~]

.

(2)

m is the electric dipole operator and & is the degeneracy of the ground state. The summation is over all components of the initial state (Aa) and final state (JA). The dipole strength DO is given by

The absorbance AA and A is

is A = yEh(&)DOcd,

the ratio

of

AA COPBH -__=---A

DokT ’

Values of C, and Do were calculated from the spectra by a moment analysis and using eq. (4). For some transitions Do is independent of temperature, for others Do increases with increasing T (fig. 7 and table II). The dipole strength of a number of transitions shows a small but significant dependence on magnetic field; an example is given in fig. 8. For three bands (transitions to 4Tz, (4D), 4E,(4D) and 4T1.J4P)) the M.C.D. signals in the paramagnetic region have indeed the temperature dependence expected for C-terms; values of Co/Do are given in table II. For large

H.J. W.M. Hoekstra et al. I Optical absorption and magnetic circular dichroism of Mnh

66

Q

10

c

u_..__-L-

28500

-I-I

29000

29500

30000

O- (cm-I) Fig. 6. Absorption A and AA of the 4T1,(4P) transition of Mnl2 for H = 4.0 Tesla, T = 4.0 K (-) and T = 1.7 K (-----); d = 40 )Lm.

15

0 D LD I

L-L

25200

26000 (7 (cm-1)

05 1

270()O

Fig. 5. Absorption A and M.C.D. AA of the q&D) (left) and 4E,(4D) (right) transitions of MnI2 for H = 4.0 Tesla, T=4.1K(--)andT=1.6K(-----);d=4O~m.

values of H/T saturation effects occur (fig. 9). The M.C.D. of the other bands (transition to 4T1, (4G), 4T29 (4G) and 4A1,, 4E, (4G)) is small and shows an anomalous temperature dependence. For two bands 4T1, (“G), 4T2g(4G) even a change of sign with increasing temperature is observed (table III). At temperatures below 3.6 K a circular di-

L

100

200

Go

T IKI

Fig. 7. Temperature dependence of the dipole strength D,l of the ‘Alg -+4TIB(4P) (0); 6A1, -+4E, + “T2,eD) (A); ‘AIs-+ 4A~, + 4E, + “r~s(~G) (Cl) and ‘Al* -)4T18(4G) (+) absorption bands of MnI2. The dashed line is the temperature dependence &(T)/&(O) = coth (hwJ2kT) for the vibronic mechanism with ou = 125 cm-’ [22].

chroic signal was observed for all absorption bands in zero magnetic field. Such a C.D. signal has been observed also in MnC12 [6] and MnBr2 [7]. Due to the magnetic ordering the symmetry

H.J. W.M. Hoekstra

et al. I Optical absorption and magnetic circular dichroism

Final state

C,lD,

4T,8(4G)


4Tz&G) 4Ar,, 4E,(4G) 4T2,(4D) “W4D) ‘T,&P)

2

67

Table II Temperature dependence of dipole strength Do and values of C,,/D,, of the transitions in MnI2

g”,--1

of MnI2

3

4 4 4 2 2 1

4 Table III The integrated M.C.D. signal AA (a.u.) ?z~(~G) transitions for H = 4 T

H(T) Fig. 8. Field dependence of the dipole strength points give observed data for T = 3.8 K for the (peak 1 in table V) of the 6Ar,--t4Eg(4G) transition. give the theoretical field dependence of Do for induced transitions in an ion pair.

1.0 1.0 1.0 1.5 1.5 2.4

Do. The first peak The lines exchange

7.5 K 18.5 K 28.5 K

of the crystal is lowered, and the crystal becomes birefringent. In a biaxial crystal a circular polarization is transformed completely or partly into a linear polarization and vice versa. In this way apparent circular dichroism can be detected as a result of linear dichroism. This interpretation of the observed zero-field C.D. in Mn12 was confirmed by measuring the linear dichroism directly. The linear dichroism signal is related to the antiferromagnetic ordering; the measurements enabled us to determine accurately the

and

+6.0 -1.7 -1.8

transition temperature: TN = 3.6 ? 0.1 K. The origin of C.D. and M.C.D. signals is quite different, and in the antiferromagnetic phase the two effects are independent and additive [15]. Below TN the sharp peaks in the spectra show shifts (of up to 10 cm-‘) as a function of the temperature. These shifts are caused presumably by exchange fields in the magnetically ordered

1.0

0.5 H/T Fig. 9. The integrated M.C.D. signal of the ?rs(‘P) (+), ‘EJ’D) represents the theoretical dependence AA = AA&&pBH/kT).

+1.6 -0.2 -0.4

of the ?t8

(T/K)

(0) and the *r&CD) (A) transitions as a function of H/T. The full curve

68

H.J. W.M. Hoekstra

et al. I Optical absorption and magnetic circular dichroism

of M&

20050

5

z.-

VI

z 20040 is

2.0

2.5

3.5

3.0

40

T(K)

Fig. 10. The position of the lowest peak of the 4A ~g,4E&4G) band as a function of temperature strength. H = 0 T: x (TN = 3.6 K); H = 2.0 T: A (TN = 3.0 K); H = 4.75 T: 0 (TV = 2.5 K).

for some values of the magnetic

field

state. The exchange fields are proportional to the sublattice magnetization, decrease with increasing temperature and vanish at TN. In fig. 10 we have plotted the position of a sharp peak of Mn12 as a function of temperature. We observe indeed the expected change of the peak position at TN. From these data we obtain TN = 3.6 K (in zero applied field). The Neel temperature TN decreases with increasing field: TN = 3.0 K at H=2T; T,=2SKat H=4.75T.

The energy levels of d electrons in transition metal ions can be calculated in terms of the Racah parameters for electron-electron repulsion, the crystal field 10Dq and the spin-orbit interaction. The Racah parameters are reduced with respect to the free ion values B,, and C, [19]. The antibonding molecular orbitals are

4. Assignment

where (Pi and pt are pure d orbitals of the metal ions and As, AU and x,, are linear combinations of ligand s, p(o) and p(r) orbitals, respectively. N: and NF are normalization factors given by

of the spectra

In Mn12 the Mn” ions are surrounded by a trigonally-distorted octahedron of iodine ions. The trigonal distortion is quite small and therefore we expect that in first approximation the absorption and M.C.D. spectra can be explained in terms of an octahedral crystal field model. Although the trigonal distortion may be small, the vibrational spectrum of these layered compounds is highly anisotropic [16]. The effect of this anisotropy has been observed clearly in the vibronic structure of the ‘AZg-+ ‘E, transition of Ni2+ in Cd12 [17, 181. Similar effects are expected in the spectra of Mt&. The assignment of the absorption spectrum of Mn12 up to 30000cm-’ has been given by Van Erk and Haas [8]. We observed the M.C.D. spectra of these absorption bands. We also found weak absorption and M.C.D. signals between 23.000 and 25.200 cm-‘; these are assigned to the excitation to a ‘T&I) state.

9: = (N:)-“*(%

- A& - A&)

>

de = W~)-“*GPt - LX?,),

N:=

l-2A,S,+A2,,

N; = 1 - 2A,S, - 2A,S, + A2,+ A:.

(5) (6)

(7) (8)

The covalency parameters A,, A,, and A, are determined by the interaction of metal d and ligand orbitals, the overlap integrals are S,, S, SIT. For these wave functions, and assuming that terms containing ligand orbitals give no contribution to the electron-electron interaction, we obtain B,,/& = CJC,, = (l/N:)2(N:/N:)“‘*,

(9)

where n is the number of e orbitals in the Slater integrals for electron-electron repulsion, and B,,, C, are the free ion Racah parameters.

H.J. W.M. Hoekstra et al. I Optical absorption and magnetic circular dichroism of MnZz

For 3d electrons in a ligand field of octahedral symmetry there are two different spin-orbit coupling constants 6 and 5’ for matrix elements between two tzg orbitals and between a tzg and an eg orbital [19]: t = (N-Y& 5’ = w:~:)-‘%

3

(10)

- 1AAALp) .

(11)

+ N!Lp)

As the spin-orbit coupling constant of iodine Sp-orbitals L&, is very large (tp = 5070 cm-‘) we expect considerable deviations from the free ion value & = 350 cm-‘. The matrix elements of the Coulomb interaction for sextets and quartets are given by terms of (reduced) Racah Pappalardo in parameters B and C [4]. Matrix elements for the doublet states could be derived from the calculations of Bird et al. [20]. The spin-orbit interaction was calculated with the aid of reduced matrix elements given by Sugano et al. [19] and the 0 coefficients for spin-orbit coupling given by Griffith [21]. The latter coefficients had to be adapted partially because there is a difference in the definition of reduced matrix elements, and the phases of the functions are not the same in refs. [19] and [21]. The energy levels calculated in this way are for transitions without change of nuclear configuration (vertical transitions in a Franck-Condon diagram). These energies should be compared with the energy of the maximum of bands broadened by vibronic interactions. In the calculations only interactions within the d’ configuration are taken into account. This will lead to errors especially for states close to the charge transfer states. The covalency will not be the same for all levels, because the covalent mixing of metal d and ligand p orbitals (the covalency parameters A,, A,, A,) depends on energy denominators which are different for different states. Therefore, strictly speaking, a description with one set of covalency parameters A,, A, A,, and one set of Racah parameters B, C is not allowed. In the calculations we have put (WIN:) (= 1 - E ; see also section 9) equal to unity as variation of this parameter did not yield any improvement.

69

The parameters B, C and 10 Dq were determined by comparing the centers of gravity of the absorption bands with the calculated values. The spin-orbit parameter 5 could be determined accurately from the splitting of the *Tt#I) band in the M.C.D. spectrum (fig. 4). This level in Mn12 belongs almost completely to the t& configuration and consequently its splitting is almost independent of L/, On the other hand, 5’ was calculated from the spin-orbit splitting of the 4T2,(4D) and 4E,(4D) levels. In the M.C.D. signal of the 4T1J4P) band some fine structure was observed. The position of this peak could not be brought into accordance with our calculations simultaneously with the splitting of the 4T2g(4D) and 4E,(4D) bands. This discrepancy is probably due to interactions with charge-transfer states. The procedure, outlined above, was repeated several times until no further improvement could be obtained. The best results are given in table I. The 4E,(4D) absorption band consists of a number of equally spaced peaks, with a spacing of 105 cm-‘. Almost the same spacing (108 cm-‘) is found in the 4T2,(4D) absorption band. These spacings correspond closely to the at-phonon of 112 cm-‘, observed in Raman spectra [22]. The small differences could be due to different force constants of ground and excited states. The 4E,(4D) level belongs to the same configuration as the ground state (t&e@, and we would expect only a weak vibronic coupling. The fact that we observe nevertheless an appreciable vibronic progression indicates that the 4E,(4D) interacts with charge-transfer states. Vibronic progressions are observed for at least two spin-orbit components of 4E,(4D) (see M.C.D. spectrum in fig. 5). The calculations predict only a small splitting between 4A,, and 4E,(4G); a detailed discussion of the assignment of peaks in this spectral region will be given in section 9. In MnCl, and MnBr2 [3,4] weak lines were reported at 78 K at the low-energy side of the absorption bands which show a pronounced vibronic fine structure. These bands were assigned to zero-phonon magnetic dipole transitions. However, the distance between these lines and the first stronger peak just corresponds to the frequency of an alg phonon in MnC12 and MnBr2 [23]. Therefore we assign these weak lines to

70

H.J. W.M. Hoekstra

et al. / Optical absorption and magnetic circular dichroism

“hot” bands corresponding to the emission of an alg phonon at 78 K. This also explains why we did 5. Theory of magnetic circular dichroism

not observe tra at 5 K.

of vibronically

similar

of MnZz

weak lines in the Mn12 spec-

induced transitions

We discuss the M.C.D. of vibronically induced electric dipole transitions of Mn2+; the spin forbiddeness is relieved by spin-orbit coupling. In an octahedral complex the ungerade vibrations which break the parity selection rule are the t,, and t2” type vibrations. The analysis is based on a paper by Vala, Rivoal and Badoz [24]. These authors calculated M.C.D. parameters for magnetic dipole transitions and vibronically induced electric dipole transitions for four types of mechanisms. However, their tables for the electric dipole transitions contain some errors. We also carried out calculations for mechanisms with intermediate states of A,, and E, symmetry; these cases were not treated by Vala et al. [24]. The classification of the vibrations in terms of t,, and t2” symmetry is not valid in Mn12. The site of the Mn2+ ions has trigonal symmetry and therefore the local vibrations can be classified as a2” and e,. Translated to octahedral symmetry this means a different coupling for the t,, +- 1 (i = 1,2) components and the ti,O component (using trigonal basis functions). The influence of the anisotropy of the vibronic coupling on the calculation of the M.C.D. parameters can be taken into account by giving a different weight to contributions from ti, t 1 and t,O components. In our calculations we multiplied the matrix elements for ti, t 1 vibrations with a factor g. It has been shown that the vibronic coupling of electronic states is much stronger with the tl, * 1 modes than with the t,,O mode, i.e. g S 1. This is due to the effect of induced dipoles at the iodine ions [17].

%I

1

&U

m

6A,g

i-i

P

case C

6A,g ’

HSO4r

,Hv, “rg

m

coupling (Hm) which make the electric dipole transitions in high spin d5 Fig. Il. Possible combinations of vibronic (Hv) and spin-rbit complexes allowed. The dotted lines indicate the optical d-d transition ‘AI, + 4r,.

H.J. W.M. Hoekstra

et al. I Optical absorption

and magnetic circular dichroism

of Mnlz

71

In the calculations six types of intensity borrowing mechanisms are considered (fig. 11). The first two types involve vibronic coupling of the excited “r, state with a 4ru, and spin-orbit coupling of the ground state with a 4T,, state (mechanism I) or spin-orbit coupling of “r, with bTlu (mechanism II). In the case of mechanism III parity forbiddenness is overcome by vibronic mixing between 4T,p and “r,, states, together with spinorbit interaction between ‘Ai, and 4T Ig states. Mechanism IV involves vibronic mixing between ‘A,, and a @Iiu or ‘TZu state, and spin-orbit coupling of the latter with 4r,. Mechanisms V and VI involve spin-orbit coupling of excited states “r, with charge transfer states 6r;, and vibronic coupling of “& with hT,, (mechanism V) or vibronic coupling of 6A,g with Y,, or ‘TZu (mechanism VI). The magnetic moments of the ‘A,, ground state are given by the spin-only values and the calculation of C,, and O,, [2S] reduces to the evaluation of matrix elements of the type

for transitions to the different spin-orbit components of the excited “r, state. In these equations t and T represent the individual spin-orbit levels and their components, respectively. J is an extra parameter, used for cases in which the representation t occurs more than once in the term “r,. The components of m are labeled by /3, with p = 0, 21. Vibrational states of ground and excited electronic states are designated by va and v,, respectively. All calculations are for low temperature so that the ground state corresponds to a zero phonon vibrational state of symmetry alg_ The matrix elements were calculated using standard vibronic theory and second-order perturbation theory [19]. The formal expressions for each of the six types of mechanisms are given in table IV. Using the coupling coefficients for trigonal basis functions given by Asada et al. [26] (see also appendix A), the V-coefficients listed by Griffith [21]*, the V-coefficients (3j symbols) given by Edmonds [27] and the Wigner-Eckart theorem [21], these expressions can be evaluated. Inspection of the symmetry dependent part shows that the mechanisms I and II give the same relative M.C.D. parameters; the same is true for mechanisms III and IV, and also for mechanisms V and VI. * Corrections are given in ref. 17. Table IV Evaluation of the matrix element (6A,~MsalmB141’,Jt~). The symmetry, etc., i = 1 or 2

c

c

+r,.hw Vuww

summation Dr.

(hA~,M,aIH,l61i.M:y’~(67,,M:y’lH,l4T,M:y”)(4T~M:y”lm~l4~gJt~) @(‘AI,)

- E(qiu)l[E(6A,,)

- E(4ru)l

is over all possible intermediate

states of 4rU

72

H.J. W.M. Hoekstra

As an example

we evaluate

X(4T~,Wy’l

et al. I Optical absorption and magnetic

the matrix

u~“~4r”M~~“)(41’“M;ly”~m~

element

circular dichroism

for mechanism

III with a tl,, vibration:

(4al,)l Q%l4td~>

tJrdfT)[E(6A

) _

E(4T

IEt

l+a+5/2-MS [C-l)’

of MnIz

)][E(hA Ig

) _ IEz

E(4J’

”

)]

1]Tlp+Y’+r,+Y”(4rg~~y”‘14~g~~T)

with

(14) In these equations we have used the fact that the electric interaction is written as

dipole operator

transforms

as Tr,. The vibronic

(15) where S is the component given by (211: X5<,.= 2

of the t,, vibration

with normal

&U.(k)

coordinate

Q Ilu. The spin-orbit

interaction

is

(16)

k=l

with the summation over all electrons The transition moments of the other mechanisms can be evaluated in a similar way*. In the calculations we have neglected differences in the energy denominators caused by spin-orbit splitting. As the spin-orbit splitting of the charge-transfer states may be several thousands cm-r in Mn12, appreciable errors may be introduced in this way in the calculated M.C.D. parameters. At large values of H/T the M.C.D. signal is no longer proportional to C,,H/kT [ll], and extra information can be obtained by comparing calculated M.C.D. signals with the results of experiments carried out at strong magnetic field and low temperature. Theoretically, if we neglect second-order spin-orbit interactions between different states and the contribution of spin-orbit interaction to the energy denominators, the M.C.D. signal summed over all spin-orbit components of an excited state is proportional to the magnetization. Therefore one expects for a paramagnet with S = 5/2

AA = AA&&&f/W,

(17)

where B, is the Brillouin function and Fa the Bohr magneton. This equation holds for all mechanisms I-VI and also for magnetic dipole transitions. The M.C.D. signals of the separate spin-orbit components generally show a different behaviour. The observed temperature and field dependence of most of the transitions agrees approximately * A complete list of calculated G, and D,J values is available on request.

73

H.J. W.M. Hoekstra et al. / Optical absorption and magnetic circular dichroism of Mnh

with the calculated behaviour (fig. 9). However, anomalous dependence of AA on T (table III).

6. Theory of exchange-induced

the transitions

6A1,+“T1g(4G)

and 4T2g(4G) show an

transitions

The theory of exchange induced electric dipole transitions has been discussed in considerable detail in the literature [lo, 28,291. In this section we confine ourselves to a discussion of two effects observed in the spectra of the paramagnetic phase, i.e. the dependence of the oscillator strength on magnetic field, and the anomalous temperature dependence of the M.C.D. Both effects were observed for Mn12 (fig. 8 and table III), and are typical for exchange induced transitions. The operator for exchange induced transitions in a pair of ions a, b is (18) ijkl

In this equation p refers to the polarization of the light, s, and sb are spin operators of electrons on ion a and b, respectively; the electron orbitals are specified by the indices ikjl (see [29]). The optical absorption to be discussed involves a transition from a ground state of the ion pair IS,S,,S’M.) to an excited state Ir$,SbS”n/i,“). In the ground state both ions are in the 6A1, state with S, = Sb = 5/2; the total spin is S’ = 0, 1,2,3,4,5. In the excited state ion a is in a state Si = 3/2; the total spin of the excited state is S” = 1,2,3,4. The transition moment is (S,s6S’MslpclryS:S,S”M~)

= s

1

i,kTZ, T!$ik).

bcii~(s~lls,,ik~l~ys:>(sb~lsb~lsb)

(19) Thus

the

selection rule is AS=S”-S’=O, S’ has the values 0, -217, 1/5a, I tively [29]. The total oscillator strength is f =

fo c

as,

S’, MS

AM=Ms,,-Ms=O. - 1/5L&?‘,

1/3fi,

The

6-j

symbol

0 for S’ = 0, L&3,4,5,

MS1 Ws12

and depends on the occupation probability ~s,M~ = exp- (E,,~~lk7’) of the ground (S’, MS) of the ion pair. The energies E S,M~ depend on the exchange interaction -2JS,& applied magnetic field Es’M~ = -J[S’(S’

+ I) - S,(S, + 1) - S,(Sb + I)] + 2pBM,.H.

Wsz

rqec-

(34 state levels and on the

(21)

From these equations we can calculate the temperature and the field dependence of the oscillator strength. We find that the field dependence is a very sensitive function of J; an example is given in fig. 8. Although the total M.C.D. signal of exchange induced transitions, integrated over all spin-orbit components, vanishes, a small signal is possible due to spin-orbit interaction with other states. As an example we calculate the M.C.D. of a 6A1s, 6A1,+4T1g, 6A1, transition of an ion pair, taking into account spin-orbit interaction of the 4Tle with a “T% state. The matrix element is

74

H.J. W.M. Hoekstra

et al. I Optical absorption and magnefic circular dichroism

of MnIz

(S,S~S’M~~~~~I~,T,Y’S~S~S’MS)(~,T~Y’S~S~S’MSI~,,I~~TIYS:MS;S~M~) in which w, and w2 specify

=

c

the configuration

of the 4T1 and 4T2 states.

Using

eq. (19) we obtain

Us,,g(S’, MS,y, y’, MS,, MS,,)Ws

For the M.C.D. AA=AA” =AAo

(22)

(23)

signal we obtain C %~s.k~(S’, s’.MsMsg. Msb,Y’

MS, y, y’ = 1, M,,, MsJ - g2(S’, MS, y, y’ = - 1, M,,, MS)} W;.

c a&(~){g2(Sr, s’.MS>MS,,Y

Ms.= S’, y, y’= 1, Ms;, MS,)

-g2(S', Mb= S’, y, y’ = - 1, MS;, MS)} W’,. , where as = E,. (Ys’,MF,Bs is the Brillouin in eq. (24) we find

function,

and AA~ = I LJz{12- I U;:12. Carrying

(24) out the summations

with ((S’) = -3120, l/30, 7140, 3/10 for S’ = 1,2,3,4, respectively. From these equations we can calculate the temperature dependence of the M.C.D. We find that the temperature dependence of the M.C.D. of exchange induced transitions is more complicated than for single ion transitions, and that the M.C.D. signal can change sign as a function of temperature, as observed for the 4T,, and 4T2g(4G) transitions (table III). 7. Discussion of the mechanism in MnIz

of d-d transitions

In this section we discuss in some detail the mechanism of the optical d-d transitions in Mn12 in the paramagnetic region. In the first place, we consider zero-phonon magnetic dipole transitions. The oscillator strengths calculated for transitions of this type are f = 10A9, and are much too small to account for the observed absorption bands in Mn12 (f - 10e5). Furthermore, the M.C.D. parameters for magnetic dipole transitions are not in agreement with the experimental data. A second possibility is that the excitations are caused by one-phonon electric dipole transitions. In this case the dipole strength is proportional to

coth (hoJ2kT), and therefore increases with increasing temperature (w, is the frequency of the ungerade phonon) [30]. A third possibility is a cooperative mechanism involving exchange interactions between adjacent Mn2+ ions as observed in MnF2 [5,29,31]. For this mechanism one expects only a small temperature dependence of the oscillator strength in the paramagnetic region [32]. of the dipole strength is smaller than expected for the vibronic mechanism (with a frequency w, = 125 cm-‘, [22]). This indicates that the vibronic and the exchange mechanism both contribute to the absorption process, but that the relative proportion of the two contributions depends on the nature of the final state. For most of the observed bands the increase

H.J. W.M. Hoekstra et al. / Optical absorption and magnetic circular dichroism of MnI2

In table II we have listed for the various transitions the temperature dependence of the dipole strength, the (Co/Do) ratio and the change AL of the orbital quantum number of the corresponding free ion states. We observe that both the M.C.D. and the temperature dependence of the dipole strength are small for AL = 4, indicating mainly exchange induced transitions in these cases. This effect can be explained in the following way. In the free ion the states are characterized by an orbital quantum number L. In the crystal L is no longer a good quantum number, because the crystal field mixes states of different L. However, if the crystal field is not too strong, the electronic states will still consist mainly of wave functions characterized by the value of L of the corresponding free ion state. The vibronic coupling is expected to be strongest for cl,-type vibrations, because this type of vibrations modulates directly the metal-ligand distance [33]. A tl, vibration normal coordinate Q corresponds mainly to L = 1, and in first approximation vibronic matrix elements will be non-vanishing only between states for which AL = 0, %l. The selection rules for spin-orbit interaction matrix elements and for electric dipole transitions are AL = 0, 21. These considerations show that it is not possible to bridge a change of AL = 4 between initial and final state by the combined effects of spin-orbit interaction (AL = 0, %l), electric dipole (AL = 0, ?l) and vibronic coupling with a ti, vibration (AL = 0, 21). Therefore one expects the vibronic contribution to transitions with AL = 4 to vanish in first approximation; small contributions can be due to the mixing of states with different L by the crystal field, and to coupling with tzU vibrations. The dipole strength of most transitions depends on the magnetic field, a behaviour which is typical for exchange induced transitions. A comparison (fig. 8) of the field dependence of the oscillator strength of the first peak of the 6A1, + 4E,(4G) transition with curves calculated for exchange induced transitions in a pair of ions (eq. (21)) suggests an exchange constant of about J = -0.25 cm-‘, We remark, however, that in Mn12 no isolated ion pairs occur, and that

15

exchange interactions with all neighbours should be taken into account. Therefore the agreement has only qualitative significance. Many mechanisms are possible for the 6Ar,+ ‘T2J21) transition. We expect that this transition is made allowed by one of the mechanisms mentioned above together with the mixing of doublets and quartets belonging to charge transfer states. This is confirmed by the fact that the oscillator strength is about 10 times larger than is expected on the basis of mixing of doublets and quartets of the d5 configuration only. Another contribution might be caused by biquadratic exchange induced electric dipole transitions [28].

8. Interpretation

of the M.C.D. data

The selection rules for spin-and parity-forbidden electric dipole transitions induced by exchange interactions between neighbouring ions, are AS = 0 and AM, = 0, where S and MS are quantum numbers of the total spin of the pair of ions. As a consequence the M.C.D. signal will vanish in first approximation for exchange induced transitions [34]. A very weak signal might be caused by spin-orbit interactions (see section 6). Therefore we attribute most of the observed M.C.D. to the vibronically induced part of the transitions and in this section we try to explain the observed sign and strength of the M.C.D. of the absorption bands. The calculation of the M.C.D. parameters for the vibronically induced transitions does not distinguish between mechanism I and II, III and IV, or between V and VI. However, we expect mechanisms II and IV to be more important, because these involve the large spin-orbit interactions (&, = 5070 cm-l) with charge transfer states. From the expressions in table II one deduces that mechanisms II and V are important especially for final states close to the charge transfer states. The C,/&values, obtained from experiments on Mn12 (Table II), will now be compared with calculated values. The Co/Q, values of the 4T2J4D), 4E,(4D) and 4T1J4P) transitions are of the same order as the values calculated for vibronically induced transitions. For the “Tl.J4G),

76

H.J. W.M. Hoekstra

et al. I Optical absorption and magnetic circular dichroism

Td4G) and 4A1,, 4E,(4G)

transitions the CO/Do values are much smaller, indicating that the absorption for these bands is mainly exchange induced. The M.C.D. signal of the 4Ti,(4G) transition is strongly temperature dependent, indicating a dominant C-term contribution. A striking feature is the fact that the M.C.D. signal changes sign within the band (fig. 2). This indicates that this band consists of unresolved components which have M.C.D. signals of different sign. Taking account of the calculated spin-orbit splitting (fig. 2 and table I) we find that the M.C.D. pattern is as predicted by mechanism B with an intermediate state 4T1Uand a t,, vibration (we abbreviate this as B(4Tl,/t,,)). The contribution of other mechanisms cannot be excluded (see also fig. 11). The 4T2g(4G) transition has almost the same M.C.D. pattern as the 4T1,(4G) transition. Inspection of the M.C.D. spectrum (fig. 2) the calculated spin-orbit components and calculated M.C.D. parameters shows that the M.C.D. spectrum of 4Tz9(4G) cannot be caused by a combination of mechanisms involving t,,-vibrations only. The dominating intensity mechanism in this case appears to be B(4T&J. This is not really surprising, as the contribution of ti, coupling is

Table V Fine structure of the 6A is +4Ai,, at about 22047 and 22330cm-’ n ai,@ = 0, 1,2); the exchange energy of a magnetic excitation. Number peak

expected to be weak because of the AL selection rule. From a comparison of the observed M.C.D. and the calculated CO/DO parameters, it follows that one cannot assign the other d-d transitions to a single dominating mechanism. Apparently, several intermediate states contribute. Also, as these transitions are closer to the absorption edge for charge transfer transitions, the contribution of spin-orbit splitting of the charge transfer states (which is neglected in the energy denominators) can be important. The M.C.D. of the hAlg+4T,g, 4T2,(4G) transitions shows an anomalous behaviour: the total M.C.D. of both bands changes sign when the temperature is changed at some fixed magnetic field strength (table III). These transitions are mainly exchange induced, and the anomalous temperature dependence of the M.C.D. can be explained by the theory given in section 6.

9. Discussion of the ‘jA1,+ 4Alg, 4EJ4G) transitions The transition to the 4A,,, 4E(4G) states of Mn*+ ions has been studied extensively. The spectra due to these transitions show a com-

4Es(4G) transitions in MnIr at T = 3.8 K and H = 4 T. The pure electronic transitions are found for ‘E, and 4A igr respectively, the vibronically induced transitions are 4E + e., 4Ai + e, + induced transitions are 4E+ m, 4Ai + m + n ais. The phonon energies are e, and ais, m is the

Frequency in the abs. spectrum (cm-‘)

Frequency in the M.C.D. spectrum (cm-‘)

Sign of the M.C.D.

Assignment

I

22047 =22oI?Q

22038

_

2 3 4 4’

22180 =22330 22360

22180 22334 22364 22456

_ + _ +

5 5’ s*

22483

4E 4E+nt 4E+e, 4A, 4A, + M “AI + e, 4A,+m+ai,

22490 22558

_ +

6 6*

22582

6** 7 7*

of

of Mnlz

22591

_

22658

+

22689

_

1 4Ai + e, + air 1 4Af + m + 2a,, 4A~ + e, + 2a,, “Ai + m + 3ai,

22683 I

H.J. W.M. Hoekstra et al. / Optical absorption and magnetic circular dichroism of Mn12

plicated fine structure which cannot be explained in terms of a simple vibronic progression. The spectra of MnFz [5,35,36,37] and Mn substituted in KZnF3 and KMgF3 [29,34,36] have been analyzed in terms of magnetic dipole transitions and exchange induced transitions. The spectra of MnF2 are strongly influenced by magnon and exciton dispersion. For unraveling the data extensive use was made of M.C.D. data and absorption spectra of exchange coupled Mn*+ pairs. Absorption data for this spectral region have been reported also for MnC12 [4,6,38], MnBr2 [4,7,38] and Mn12 [8,22], but a detailed analysis has not been given so far. The absorption and M.C.D. spectra of the 4A,,, 4E,(4G) band of Mn12 are shown in fig. 3; the frequencies of the observed peaks are given in table V. The peaks in the absorption spectrum were assigned by Van Erk [8] to three progressions of alg phonons, with origins at 22062, 22105 The origins at 22062 and and 22373 cm-‘. 22105 cm-’ were assigned to 4E,(4G), that at 22373 cm-’ to 4A1,(4G). The 4A1,-4E, splitting was attributed to second-order spinorbit coupling with the 2T5g(21), the splitting of 4E,(4G) into two components to higher-order spin-orbit interactions. The states 4A1, and 4E,(4G) are degenerate in first approximation; a lifting of the degeneracy can be produced by covalency or second-order spin-orbit interaction. Because we have been able to measure directly the position of the ‘T$eI) state, it was possible to calculate the contribution to the 4A1,-4E, splitting due to interaction with *T&(ZI); the result is only a small splitting, of a few cm-‘. Therefore we conclude that the 4A,,-4E, splitting cannot be due to second-order spin-orbit interaction. The effect of covalency has been discussed by Van Erk in terms of a covalency parameter I introduced by Koide and Pryce [39]. It can be shown that this effect can lead only to a small splitting of less than 110 cm-‘. However, Lohr [l] has given a more detailed description of the influence of covalency in terms of two parameters ft and fe, for the effect on t2, and eg orbitals, respectively. For reasonable values of the parameters, it is possible to obtain values of the 4A,g-4Eg splitting similar to the observed values.

77

Therefore we conclude that the splitting E(4A1,)be due to E(4E,) = 291 cm-’ in Mn12 must covalency, and that the contribution of spinorbit splitting is small. Because of increasing covalency the 4A1,-4E, splitting increases in the series MnF2 (143 cm-‘, [37]), MnC12 (235 cm-‘, [6]), MnBr2 (=300 cm-‘, (381) and MnI2 (291 cm-‘). A calculation (table I) shows that the effect of second-order spin-orbit interaction is too small to explain the width or apparent splitting of 4E,(4G) into two peaks in Mn12. We now proceed with the assignment of the peaks in the 4A1,, 4E,(4G) spectral region. Transitions are due to zero-phonon magnetic dipole transitions, vibronic interactions with ungerade phonons, and exchange induced transitions. According to the temperature dependence of the oscillator strength, we expect that most of the oscillator strength is due to exchange induced transitions. The M.C.D. spectrum, however, will be dominated by magnetic dipole transitions and by vibronically induced transitions, because the M.C.D. of exchange induced transitions is weak. At T = 2.3 K we observe a sharp M.C.D. signal at 22038cm-‘, which we attribute to the zero-phonon 4E,(4G) magnetic dipole transition. The negative M.C.D. signal is expected for this transition. The absorption band in the same region has also a broad and asymmetric component (width -100 cm-‘), which we assign to zero-phonon exchange induced 4E,(4G) transitions. The width of the band can be due to magnon and/or exciton dispersion [5]. At higher energy the spectrum shows a relatively sharp band (peak 3, at 22334 cm-‘) with a positive M.C.D., which we attribute to a zerophonon magnetic dipole transition 4Alp; the positive M.C.D. signal is expected for this transition. The vibronic progression (peaks 4*, 5**, 6**) is only observed in M.C.D.; it has a positive M.C.D. and is attributed to vibronically induced transitions. The origin 4* of this progression has a frequency E (4A,,) + hw(e,), where hw(e,) is the energy of a e, phonon (i.e. the -cl components of the tl, phonon of the octahedron). The energy ho(e,) = 125 cm-’ was obtained from infrared spectra [22]. The other peaks 5**, 6** of this progression have energies

78

H.J. W.M. Hoekstra et al. / Optical absorptionand magnetic circulardichroismof MnIz

J!Z(~A,,) + ho(e,) + nhw(ar,), with II = 1,2. Finally we observed a strong progression (peaks 4,5,6,7) in the absorption spectrum; this progression has a weak negative M.C.D., and is to exchange induced transitions assigned E(4A1,)+ nhw(a3 (n = 0, 1,2,3). In exchange induced transitions an exciton (wave vector k,) and a magnetic excitation (wave vector k,) are produced simultaneously. The selection rule for the transition is k, + k, = 0, the energy is F = E0 + E,(k,) + E,,,(k,). Exchange interactions in MnX2 (X = Cl, Br, I) are weak and therefore the energies of magnetic excitations will be small (only a few cm-l). The dispersion of 4E,(4G) excitons in Mn2+ compounds, on the other hand, can be quite large [35]. Therefore we attribute the width of the band of exchange induced transitions to exciton dispersion, and neglect the contribution of the energy of magnetic excitations. The shape of the absorption band will be related to the density of exciton states. The Mn-dihalides are layered compounds; the cations occupy octahedral holes in a close packing of anions, and form hexagonal layers. Exciton dispersion is given by

b

two sites it and where b is the vector connecting rt + b, and (&lx]&+b) is the hopping integral for transfer from site n to II + b. For a simple hexagonal lattice, taking into account only hopping between neighbouring sites, we obtain E,(k) = Eo + t[2 cos k,a + 4 cos(i k,a)cos(i

k,aVQ)]

.

(27)

The exciton energies spread over an energy range 9 t. A complication is that in the paramagnetic region the excitons move in a random lattice of spins. Transfer of excitons is possible only between sites with parallel spins. This reduces the hopping integral to a smaller value teR= t cos2(8/2), for transfer between sites with spins which make an angle 8 with each other [4Q]. This

effect breaks up the exciton band and reduces the band width. In a paramagnet the average value (cos2 19/2)= 1, so that teR= it. The absorption bands 4E, in MnCl,, MnBr;! and Mn12 in the paramagnetic region are similar in shape and width. The width of about 80 cm-’ in Mn12 corresponds to teff-9 cm-’ for the effective hopping integral of an 4E, exciton to a neighbouring site. This value is comparable to the results obtained for MnF2: for hopping in the c-direction a value of t = 18.5 cm-’ (=$K,) was deduced from the spectra [35].

10. Conclusions The d-d optical transitions of Mn2+ in an octahedral coordination, although doubly forbidden by parity and spin selection rules, are fairly intense. This is so in particular for Mn2+ compounds with highly covalent ligands, such as MnS and Mn12. The explanation of this is directly related to the mechanism of the d-d transitions. We have studied absorption and M.C.D. spectra of Mn12, and obtained the following evidence on the mechanism of absorption in the paramagnetic region: a) the spectra show vibronic progressions, and splittings due to spin-orbit coupling; b) the dipole strength of some transitions increases with temperature as expected for transitions induced by coupling with ungerade phonons; the dipole strength of other transitions is nearly independent of T, as expected for exchange induced transitions; c) in some cases the dipole strength at low temperature depends on the applied magnetic field; for two transitions the M.C.D. changes sign as a function of temperature. These effects are typical for exchange induced transitions; d) in accordance with the theory, the mainly exchange induced transitions have only a weak M.C.D. signal. We conclude that the d-d transitions of Mn12 are partly vibronic and partly exchange induced. The relative contribution of exchange and vibronic mechanisms differs strongly for the various transitions, and depends on the nature of the final state, i.e. on the change

79

H.J. W.M. Hoekstra et al. / Optical absorption and magnetic circular dichroism of MnI2

magnetic ordering of the spins at low temperature. Therefore it is quite well possible to have strong exchange induced optical transitions also in compounds with weak magnetic interactions between ions in the ground state. Neutron diffraction studies [12] indicate a complicated helical type of ordering in which the magnetic moments in (307) planes are aligned ferromagnetically but rotate by 2~/16 in successive (307) planes; a NeCl temperature of TN = 3.4K was reported [13]. We remark that the magnetic structure is deduced from only a few broad diffraction peaks; a reinvestigation could be worthwhile. Our measurements show that the transition to the antiferromagnetic phase is accompanied by the occurence of linear dichroism, and by an appreciable shift of several of the

AL of the quantum

number of the (main) atomic configuration involved. and M.C.D. spectra of the Absorption 4E,(4G) band show a complicated fine struc4AIg, ture which could be assigned to magnetic dipole vibronic transitions involving untransitions, gerade phonons and exchange induced transitions. The width of the first peak of exchange induced transitions is attributed to exciton diffusion. We point out that the non-diagonal exchange integrals responsible for the exchange-induced optical transitions involve not only d-orbitals of the transition metal ions of the ion pair but also ligand orbitals. These exchange integrals are very different from the exchange integrals between ions in the ground state, which determine the

Appendix A Coupling coefficients for the cubic double group with complex trigonal bases. Some of the coupling coefficients given by Asada et al. [26] are not correct. The corrected values are given below.

u2

-l/2

-312

312

l/2

0

0

0

0

0

-&

0

0

2d2 -iz

i&5

0

0

52

0

0

0

1

42 55

0

0

0

0

T2

0

312

-1

l/2

-l/2

312

ik

0

0

-43

0

0

0

0

-sit

0

0

0

zz

43

0

0

0

0

0

v/2 -Fz

-&

G% d5

0

0

0

ik 0

1

0

0

0

2l/2 iz

0

0

0

0

0

-1

0

0

0

sz

0

0

0

0

-%

0

2d2 7-G

-312

-$

0

0

-

0

-27

1

0

3

0

0

-A

sz

d5

0

0

-1

$5

-l/2

0

2v2 -vi%

-1

-312

u’s/2

U’3/2

U’xT2 U

4% 0 -i&

0

0

3

0

0

0 0

%

0

ii% 0

80

H.J. W.M. Hoekstra

et al. I Optical absorption and magnetic

absorption peaks. We found a NeCl temperature of 3.6 K (in zero magnetic field). For a detailed interpretation of the low temperature optical spectra more information about the ordering of the spins in the antiferromagnetic phase is required.

Acknowlegdements This investigation was supported by the Netherlands Foundation for Chemical Research (SON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (ZWO). The authors thank A. Lenselink for the computer program used for the fitting of the spectra.

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J. Chem.

Phys. 45 (1966) 361 I. J.Chem. Phys.

(21 L.L. Lohr and D.S. McClure,

4Y (1968) 3516. [Xl P. Pappalardo, J. Chem. Phys. 33 (1960) 613. J. Chem. Phys. 31 (1959) 1050. [41 P. Pappalardo, I51 D.D. Sell, R.L. Greene and R.M. White, Phys. Rev. 158 (1966) 489. 161 M. Regis and Y. Farge, J. Physique 37 (1976) 627. 171 Y. Farge. M. Regis and B.S.H. Royce, J. Physique 37 (1976) 637. 181 W. van Erk and C. Haas, Phys. Status Sol. (b) 70 (1975) 517. 191 Y. Tanabe, 7. Moriya and S. Sugano, Phys. Rev. Letters 15 (1965) 1023. and K. Gondaira, J. Phys. Sot. Japan 22 IlO1 Y. Tanabe (1967) 573. Quart. Rev. Chem. 1111 P.N. Schatz and A.J. McCaffery, Sot. 23 (1969) 552. 1974. [I21 W. van Erk, thesis, Groningen, E.O. Wollan and W.C. [I31 J.W. Cable, M.K. Wilkinson, Koehler, Phys. Rev. 125 (1962) 1860. P. Day, R.G. Denning, P.N. Quested [I41 J.C. Collingwood, and T.R. Snellgrove, J. Phys. E.: Sci. Instr. 7 (1974) 991.

circular dichroism

of Mnll

C.D. PfeilIer and W.M. Yen, I151 Y. Wong, F.L. Scarpace, Phys. Rev. B9 (1974) 3086. [lfd H.J.L. van der Valk and C. Haas, Phys. Status Sol. (b) 80 (1977) 321. P.R. Boudewijn, C. Haas, J. Beth(171 S.R. Kuindersma. lehem and A. Meetsma, Phys. Rev. B26 (1982) 40. and P.R. Boudewijn, Solid State [la S.R. Kuindersma Commun. 27 (1978) 1181. Multiplets of 1191 S. Sugano, Y. Tanabe and H. Kamimura, Transition-Metal Ions in Crystals (Academic Press, New York and London, 1970). Phil. Trans. WI B.D. Bird, E.A. Cooke and A.F. Orchard, Roy. Sot. A276 (1974) 277. Tensor Method for Mole[211 J.S. Griffith, The Irreducible cular Symmetry Groups (Prentice Hall. Englewood Cliffs, 1962). L. Piseri and 1. Pollini, Int. Conf. on WI L. Patrinieri, Raman Spectroscopy, Bordeaux, 1982. I. Pollini, L. Piseri and R. Tubino, Phys. [231 G. Benedek, Rev. B20 (1979) 4303. P41 M. Vala, J.C. Rivoal and B. Badoz, Mol. Phys. 30 (1975) 1325. P51 P.J. Stephens, Adv. Chem. Phys. 35 (1976) 107. WI S. Asada, C. Satoko and S. Sugano, J. Phys. Sot. Japan 37 (1975) 855. Edmonds, Angular Momentum in Quantum (271 A.R. Mechanics (Princeton Univ. Press, Princeton, 1957). Pa L. Dubicki and Y. Tanabe, Mol. Phys. 34 (1977) 1531. H.J. Guggenheim and Y. Tanabe, J. Phys. [291 J. Ferguson, Sot. Japan 21 (1966) 692. [30] C.J. Ballhausen, Introduction to Ligand Field Theory. (McGraw-Hill. New York, 1962). K. Petanides and Y. Tanabe, I311 T. Fujiwara, W. Gebhardt, J. Phys. Sot. Japan 33 (1972) 39. and I. Harada, Solid State Commun. 8 (321 K. Motizuki (1970) 951. [33] N.B. Manson. Phys. Rev. B4 (1971) 2656. H.U. Gildel, E.R. Krausz and H.J. GugI341 J. Ferguson. genheim, Mol. Phys. 28 (1974) 8Y3. Phys. Rev. [35] R.S. Meltzer, M. Lowe and D.S. McClure, 180 (1969) 561. f361 J. Ferguson, Austr. J. Chem. 21 (1%8) 307. J.A. Spencer, W.C. Yaeckel and P.N. I371 P.W. Schwartz, Schatz, J. Chem. Phys. 60 (1974) 2598. Phys. Rev. 822 (381 I. Pollini, G. Spinolo and G. Benedek, (1980) 6369. [391 S. Koide and M.H.L. Pryce, Phil. Mag. 3 (1958) 607. Exp. Theor. Phys. 33 (1971) WI E.G. Petrov, Sov. Phys:J. 573.